Howdy!
Most of our premium themes include a set of default fonts determined by the theme, and can only changed with the Custom Design upgrade:
http://en.support.wordpress.com/custom-design/
The fonts in Vintage Kitchen should look like the ones in the theme screenshots on the Theme Showcase page:
http://theme.wordpress.com/themes/vintage-kitchen
If you’re not seeing those fonts when you view your site, can you post a screenshot of the problem? You can find instructions for making and sharing a screenshot here:
http://en.support.wordpress.com/make-a-screenshot/
And there is no official Publish button, you just publish your first post(s) and share the link. :)
I hope this clears things up!